How do you graph and solve #|4x – 3|+ 2 <11#?

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Answer 1 · 2018-07-16T18:51:14

The solution is #x in (-3/2,3)#

The inequality is

#|4x-3|+2<11#

#|4x-3|-9<0#

The point to consider is

#4x-3=0#

#=>#, #x=3/4#

There are #2# intervals to consider

#(-oo, 3/4)# and #(3/4,+oo)#

Therefore,

In the first interval

#-4x+3-9<0#

#=>#, #-4x-6<0#

#=>0#, #4x> -6#

#=>#, #x> -3/2#

This solution belongs to the interval

In the second interval

#4x-3-9<0#

#=>#, #4x-12<0#

#=>#, #x<3#

This solution belongs to the interval

The solution is #x in (-3/2,3)#

graph{|4x-3|-9 [-20.27, 20.27, -10.14, 10.14]}